Letter
pubs.acs.org/JPCL
Density Functional Theory Study of the Interaction of Hydrogen with
Li6C60
Qian Wang†,‡ and Puru Jena*,‡
†
Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
Physics Department, Virginia Commonwealth University, Richmond, Virginia 23284, United States
‡
ABSTRACT: Hydrogen storage properties of Li-coated C60 fullerene have been
studied using density functional theory within the local density as well as generalized
gradient approximation. Hydrogen atoms are found to bind to Li6C60 in two distinct
forms, with the first set attaching to C atoms, not linked to Li, in atomic form. Once all
such C atoms are saturated with hydrogen, the second set of hydrogen atoms bind
quasi-molecularly to the Li atoms, five of which remain in the exohedral and the sixth
in the endohedral position. The corresponding hydrogen gravimetric density in
Li6C60H40 is 5 wt %. Desorption of hydrogen takes place in succession, the ones bound
quasi-molecularly desorbing at a temperature lower than the ones bound atomically.
The results are compared with the recent experiment on hydrogen adsorption in
Li6C60.
SECTION: Energy Conversion and Storage; Energy and Charge Transport
I
exciting results, however, leave some fundamental questions
unanswered. (1) For example, where do Li atoms reside in C60?
Do they occupy an exohedral or endohedral position? Do they
cluster or remain isolated? (2) As Li doped C60 is hydrogenated, where do the hydrogen atoms reside? Do they bind to
Li or C atoms and in what form? (3) What is the maximum
number of H atoms that can bind to the Li6C60 surface and
does their binding energy depend upon the amount of
hydrogen adsorbed? (4) Why does the Li6C60 cage not break
up and release hydrocarbons while the C60 fullerene does
during dehydrogenation? (5) Why does hydrogen desorb at a
much lower temperature in hydrogenated Li6C60 than in
fulleranes? In this Letter, we provide answers to some of these
questions by carrying out detailed density functional theory
based calculations. In the following, we give a brief description
of our theoretical procedure, which is followed by a discussion
of our results and a summary of our conclusions.
Site preference of Li and H atoms on C60, the total energies
of Li-decorated C60 with and without hydrogen loading, and the
electronic structure of Li6C60Hx were calculated using density
functional theory and the Perdew−Burke−Ernzerhof (PBE)16
form for the generalized gradient-corrected (GGA) exchange−
correlation functional. We used a plane wave basis set and the
projector augmented wave method as implemented in the
Vienna ab initio Simulation Package (VASP).17 The supercell
approach was used where clusters were placed at the center of a
24 × 24 × 24 Å3 cubic cell. Due to the large supercell, the
Brillouin zone integration was performed only at the Γ point.
The energy cutoff was set at 400 eV. In all calculations, self-
deal hydrogen storage materials for mobile applications
require the host material to be light and to operate at nearambient thermodynamic conditions.1,2 For the latter requirement, hydrogen binding should be intermediate between
physisorption and chemisorption. Unfortunately, lightweight
materials such as Li and C bind hydrogen strongly. For
example, in LiH, hydrogen desorbs at 670 °C,3 while in
hydrogenated C60 fullerenes, C60Hx (often referred to as
fulleranes or hydrofullerenes), hydrogen desorbs at temperatures above 500 °C.4−9 In addition, the fulleranes release
hydrocarbons during hydrogen desorption, thus making
fullerenes unsuitable for reversible hydrogen storage.5,7,10,11 It
was suggested12 that one can avoid this problem by doping C60
with Li. Because C60 has a large electron affinity, charge transfer
from Li to the C60 cage makes Li positively charged, and the
electric field produced by such point charges can bind hydrogen
through the polarization mechanism.13,14 In such a case, H2
molecules are polarized and bind to Li in quasi-molecular
form13,14 with a binding energy lying between physisorption
and chemisorption. This makes it possible for hydrogen to
desorb at near-ambient conditions. It was predicted that Li12C60
can reversibly store as much as 13 wt % hydrogen in quasimolecular form.12
Recently Teprovich et al.15 have carried out an experiment
using solvent-assisted mixing in which the mole ratio of LiH/
C60 was varied from 120:1 to 2:1. The authors found that
LixC60 was capable of storing hydrogen reversibly through
chemisorption at elevated temperatures and pressures. In
particular, Li6C60 with a mole ratio of 6:1 can reversibly desorb
up to 5 wt % H2 with an onset temperature of ∼270 °C. In
addition, the fullerene cage remained mostly intact and was
only slightly modified during the desorption/adsorption cycle.
Furthermore, no release of hydrocarbons was noticed. These
© 2012 American Chemical Society
Received: February 17, 2012
Accepted: April 9, 2012
Published: April 9, 2012
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consistency was achieved with a tolerance in the total energy of
at least 0.01 meV. Hellman−Feynman force components on
each ion in the supercells were converged to 1 meV/Å. The
structures were optimized without any symmetry constraint. In
the case of hydrogen molecules binding weakly to the Li metal
ions, calculations were repeated using local density approximation (LDA).18 This is because DFT does not treat
dispersive forces properly and GGA is known to cause
underbinding. On the other hand, LDA leads to overbinding
and somehow compensates for the lack of dispersive forces in
DFT. Test calculations have shown that binding energies in
weakly coupled systems computed using LDA are in better
agreement with those from experiment as well with those based
on second-order Moller−Plesset perturbation theory (MP2)19
and the coupled cluster method with singles and doubles and
noniterative inclusion of triples [CCSD(T)].20 We have also
performed IR stability calculations to ensure that the
geometries presented in this Letter are dynamically stable and
contain no imaginary frequencies.
Site Preference of Li As a Function of Li Concentration. We first
discuss the geometry of LixC60 (x = 1, 6). To determine the
preferred site of Li on C60, we first calculated the total energies
of LiC60 by placing the Li atom on the five-fold and six-fold
hollow sites. The preferred site is one where Li binds to the
five-fold site, while the one bound to the six-fold site is 60 meV
higher in energy. This is in agreement with earlier
calculations.12
The energy barrier when the Li atom moves from the
pentagon to the hexagon site across a C−C bridge was
calculated to be 0.35 eV by using the nudged elastic band
(NEB) method implemented in VASP code. This barrier is
larger than the 0.2 eV barrier in the (5,5) carbon nanotube21
when a Li atom moves across a C−C bridge from one hexagon
to another along the nonaxial direction. Although C60 and the
(5,5) carbon nanotube have very similar diameters, the
pentagon to hexagon migration in C60 results in a larger
energy barrier. Because this is much larger than the thermal
energy corresponding to the room temperature, Li migration is
unlikely under ambient thermodynamic conditions.
There are many possibilities for the geometry of Li6C60.
Here, Li atoms may occupy near-neighbor sites, remain isolated
from each other, or form either endohedral or exohedral
complexes. In Figure 1, we provide the optimized geometry of
four low-lying isomers of Li6C60 with Li atoms having the
freedom to occupy an exohedral or endoheral position as well
as forming isolated or clustered configurations. The configuration with Li atoms bound to exohedral sites and occupying
near-neighbor positions has the lowest energy, but the other
geometries are energetically nearly degenerate. This is because
there is virtually no interaction between the Li atoms because
the Li−Li binding energy (1.10 eV) is much smaller than the
Li−C binding energy (2.83 eV). In addition, the binding energy
per Li atom in LixC60, defined as
E b(Li) = − [E(LixC60) − E(C60) − xE(Li)]/x
Figure 1. Geometries of the ground-state (a1) and low-lying isomers
(a2), (b1), and (b2) of Li6C60 clusters. Relative energies Δε of each
cluster with respect to the ground state are also given. The symmetries
of (a1), (b1), and (a2) structures are C5v, while that of (b2) is C2.
Figure 2. (a1) HOMO and (a2) LUMO of the Li6C60 cluster with C5v
symmetry; (b1) HOMO and (b2) LUMO of the lowest-energy
configuration of the Li6C60−40H cluster.
pentagons along the C5v axis contribute more to the HOMO
but not to the LUMO, as shown in Figure 2(a1) and (a2),
respectively.
Site Preference of H As a Function of Li Concentration
(LixC60Hy). Using total energy calculations, we first determine
the preferred site of one H atom in LiC60 by placing it atop the
Li site. Next, we considered H atop the C atom nearest to the
Li atom as well as the C site farthest from the Li atom. Again,
the geometries are fully relaxed for each configuration. The
resulting optimized geometries and relative energies measured
with respect to the lowest-energy configuration are given in
Figure 3. We note that the clearly preferred configuration for
the H atom is where it attaches to the on-top C site that is
nearest to the Li atom (Figure 4b). We define the binding
energy of hydrogen as
(1)
is 1.53 eV for x = 1 and 1.76 eV for x = 6. The small difference
in Eb(Li) suggests that Li atoms may randomly occupy five-fold
sites in C60. IR stability calculations confirmed the dynamical
stability of the geometries with no imaginary frequencies. In
Figure 2, we plot the highest occupied molecular orbital
(HOMO) and the lowest unoccupied molecular orbital
(LUMO) corresponding to the lowest-energy structure in
Figure 1(a1). We find that the C atoms in the two adjoining
E b(H) = −[E(LiC60H) − E(LiC60) − E(H)]
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surface with H atoms binding to C or Li atoms [Figure 4(a1)].
Second, we allowed the H atoms to cluster over the C60 surface
[Figure 4(a2)]. In the third configuration [Figure 4(a3)], some
of the H atoms were bound to Li atoms in quasi-molecular
form, while others were bound to C atoms chemically. In these
three configurations, the Li atoms were kept on exohedral sites.
The calculations were repeated by allowing Li atoms to occupy
both exohedral and endohedral positions. Three of the lowlying isomers, optimized without any symmetry constraint, are
shown in Figure 4(b1), (b2), and (b3). The relative energies
measured with respect to the lowest-energy structure are given
in Figure 4. Thermodynamically, the most stable structure
[Figure 4(b2)] is the one where five Li atoms remain on the
outside, with each binding to one H2 molecule in quasimolecular form. The sixth Li atom becomes endohedral and
does not bind to any H atom. The other 30 H atoms bind to 30
C atoms not coordinated with Li. The degeneracy between the
Li6C60 structures with five Li atoms on the outside and one Li
atom on the inside versus that with all six Li atoms on the
outside (see Figure 1) is lifted once H atoms are adsorbed.
Note that the structure where six Li atoms are on the outside
binding to five H2 molecules [Figure 4(a3)] is 2.53 eV higher in
energy than the ground-state structure.
The ground-state structure in Figure 4(b2) is interesting.
Here, the C atoms linked to Li do not bind H. Because for each
Li atom there are five such C atoms, a total of 30 C atoms in
C60 cannot bind hydrogen. That leaves only 30 C atoms, each
of which binds to one H atom. Because Li atoms are positively
charged, they bind hydrogen in quasi-molecular fashion due to
the charge polarization mechanism discussed earlier.13,14 Thus,
five Li atoms bind five H2 molecules, and the geometry in
Figure 4(b2) completely accounts for all of the H atoms
attached in Li6C60H40. We also note that the structure of the
C60 cage gets distorted as Li and H atoms are bound.
In order to better understand the lowest-energy structure of
Li6C60H40 as shown in Figure.4(b2), where one Li atom is
inside of the cage, we calculated the energy barrier that needs to
be overcome by Li for insertion into the cage. One possible
scenario is that at high temperature, one Li atom may diffuse
Figure 3. Geometries of the ground-state and low-lying isomers of the
LiC60−H cluster. Interatomic distances and relative energies Δε with
respect to the ground state are also given.
This binding energy is 2.76 eV. This needs to be compared with
the 3.58 eV binding energy of H to C in a CH dimer and the
2.34 eV binding energy of H to Li in a LiH dimer. This
comparison establishes why H prefers to bind to C rather than
to Li. To understand why H prefers to bind to a C atom that is
nearest to the Li atom rather than to the one farthest removed,
we note that H prefers to remain as a H− ion. The charge
transfer from Li to C60 puts extra electrons in the vicinity of the
Li atom, enabling the C atoms nearest to C60 to donate
electrons to H more easily.
We next consider the geometry of Li6C60 decorated with 40
H atoms as this corresponds to 5 wt % hydrogen seen
experimentally to desorb around 270 °C. The questions that
need to be answered are as follows: (1) Where do these H
atoms reside? (2) Does the location of the Li atoms on C60
change as more hydrogen atoms are adsorbed? (3) What is the
average binding energy of H per atom in Li6C60Hx and how
does it compare to that in C60Hx? (4) Does the C60 cage remain
unaffected as Li and H atoms are loaded? To answer these
questions, six configurations were considered (see Figure 4).
We first introduced H atoms on top of Li and C atoms in such
a way that the 40 H atoms were distributed over the entire C60
Figure 4. Geometries of the ground state (b2) and the other five low-lying isomers of the Li6C60H40 cluster. Relative energies Δε with respect to the
ground state of each cluster are given.
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polarization mechanism that is not chemical in nature and
hence is weak.13,14 We should caution the reader that density
functional theory with GGA functional does not include
dispersive forces and hence always leads to underbinding.
Because DFT within LDA leads to overbinding, it is expected
that calculations at the DFT/LDA level of theory may
compensate for this omission and may yield a more realistic
binding energy when dealing with weak polarization forces. We,
therefore, repeated the above calculations using DFT/LDA
with the Vosko−Wills−Nussair (VWN) formula.24 The
resulting ⟨Eb(H)⟩ was found to be 0.28 eV, which is
significantly larger than that obtained using the DFT/GGA
formalism.
Leaving quantitative comparison aside, we can confidently
conclude that there are two types of H atoms bound in Li6C60
with very different binding energies. The ones bound more
weakly, namely, the quasi-molecular species, will desorb at a
lower temperature, while those bound more strongly to the C
atom will require elevated temperatures. We should point out
that if only the quasi-molecular hydrogen atoms are seen
experimentally to reversibly adsorb on Li6C60, the gravimetric
density should be 1.25 wt % and not 5 wt % as observed. To
reconcile this apparent discrepancy, we note that as many as
five H2 molecules can be bound12 to a Li atom in free Li12C60.
However, when the Li12C60 clusters interact as they would in a
solid-state environment, the Li atoms bonding the two C60
fullerenes cannot bind hydrogen, thus reducing their total
hydrogen uptake. Gravimetric density of 5 wt % hydrogen
storage in bulk Li6C60 can be achieved if each of the five
exohedral Li atoms can bind to four H2 molecules.
Our results also explain why dehydrogenation of fullerenes
leads to breaking up of the cage structure and emission of
hydrocarbons while similar effects are not present in Li6C60. We
recall that the binding energy of atomic hydrogen in Li6C60 is
larger than that in C60. Thus, the temperature required to break
up Li60C60 will be higher than that of C60. This may be a likely
cause for the enhanced stability of the Li6C60 cage during
repeated adsorption/desortion cycles. Hydrogen atoms that are
seen to desorb from Li6C60 at lower temperatures are those that
are bound more weakly than the ones bound in atomic form.
In summary, we have carried out a systematic and
comprehensive study to determine the site preference of Li
on C60, the sites that hydrogen atoms occupy as a function of Li
concentration, the nature of hydrogen bonding as a function of
hydrogen concentration, and their corresponding binding
energy. While Li atoms prefer to occupy exohedral sites in
C60, the structure with one Li atom in the endohedral position
is nearly degenerate. However, this degeneracy is lifted once
hydrogen atoms are present. For example, in the Li6C60H40
structure, one of the Li atoms prefers to remain in the
endohedral position. We find that hydrogen atoms bind more
strongly to C atoms in Li-coated C60 compared to that in pure
C60. There are two types of hydrogen bonding in Li6C60; the
first set of hydrogen binds to C in atomic form, and subsequent
H atoms bind to Li in quasi-molecular form. Forty H atoms can
be adsorbed on Li6C60, where 30 of them are bound to C atoms
in atomic form and 10 of them to Li in quasi-molecular form.
Because the former binding is much stronger than the latter,
this permits hydrogen atoms to desorb in successive steps. We
should caution the reader that our calculations did not take into
account van der Waal and zero-point energy corrections.
Grimme25 has pointed out that the GGA exchange−correlation
usually underestimates the binding energy by ∼0.08 eV/H2 .
from one pentagon to the nearest hexagon from which it can
enter into the cage. We, therefore, calculated this energy barrier,
which was found to be 6.95 eV. While this is very large, we note
that it is smaller than the penetration energy barrier of 7.40 eV
on a graphene sheet.22 This can be understood with the
following two factors: First, in C60, the longer C−C bond
between a hexagon and a pentagon is 1.458 Å, and the shorter
C−C bond length between the two hexagons is 1.40 Å.23 The
average C−C bond length in a hexagon is 1.429 Å, which is
larger than that (1.40 Å) in the graphene sheet. Second, due to
the curvature of the C60 sureface, the pz orbitals are orientated
more outwardly, which would further reduce the energy barrier
when the Li atom enters the cage. It is likely that under
experimental conditions,15 all of the Li atoms may reside on the
exohedral positions. In that case, the sixth Li atom can also bind
to one H2 molecule, thus increasing the number of hydrogen
atoms from 40 to 42. Note that the exact number of H atoms
attached to Li6C60 was not determined in the above experiment,
and the authors estimated it to be around 40.
Binding Energy of Hydrogen to C60 versus LixC60. As mentioned
earlier, the binding energy of a H atom to C60 decorated with a
single Li atom is 2.76 eV. In order to see how this binding
energy changes with respect to multiple hydrogen decoration,
we first consider the average binding energy of H in the
Li6C60H30 cluster. Here, H atoms are bound to the 30 C atoms
that are not linked to Li. The average H binding energy is
define as
⟨E b(H)⟩ = −[E(Li6C60H30) − E(Li6C60) − 30E(H)]/30
We find ⟨Eb(H)⟩ to be 2.64 eV. Because this is rather close to
the binding energy of 2.76 eV in LiC60H, one can conclude that
the binding energy of H is not very sensitive to the number of
Li atoms that decorate C60. To examine how these binding
energies compare with that in pristine C60, we have calculated
the optimized structures of C60H30 and C60H60 clusters. While
there is no ambiguity in the structure of C60H60 as there is one
H atom for every C atom, there are numerous choices for the
possible structure of C60H30. We considered an initial geometry
for C60H30 by removing the six Li atoms and five quasimolecularly bound H2’s from Figure 4(b2). The structure was
then reoptimized. The calculated average binding energies of
the H atom in the C60H30 and C60H60 clusters were 2.54 and
2.44 eV, respectively. These energies are slightly smaller than
those in Li6C60H30, namely, 2.64 eV. In other words, hydrogen
binds more strongly to Li-coated C60 than to pristine C60. The
question then remains, Why does hydrogen desorb from
Li6C60Hy at a lower temperature than that from C60Hy?
Thermodynamically this should not be the case because H is
bound to C in Li6C60H30 at least as strongly as that in Li6C60.
We note that in Li6C60H40, 10 H atoms are bound quasimolecularly to the Li atoms. The binding energy of these H
atoms is clearly less than that for the ones bound in atomic
form. To see what this binding energy is, we calculated the
energy needed to desorb only the H atoms bound quasimolecularly using the equation
⟨E b(H 2)⟩ = −[E(Li 6C605H 2) − E(Li6C60) − 5E(H 2)]/5
This yields a binding energy of 0.14 eV. The corresponding
energy when C60 contains only one Li atom is 0.17 eV. The
substantial reduction in binding energy between H atoms
bound quasi-molecularly versus those bound chemically to the
C atoms is due to the different mechanisms operative in the
bonding scheme. In the former, the bonding is due to a
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Zero-point energy correction, on the other hand, reduces the
binding energy by about 20%. Because these two omissions
compensate for each other, we believe that our conclusions are
qualitatively correct. We also note that while these studies are
performed on an isolated C60 cluster, experiments were carried
out in bulk samples where interaction between C60 clusters may
also be important. However, prior studies12 showed that the
structure of the Li-coated C60 remained intact during such
interactions, and three H2 molecules could still be bound to
each Li atom. We are currently carrying out studies of hydrogen
storage properties of Li6C60 cluster-assembled materials to get a
quantitative understanding of hydrogen sorption.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work was supported in part by grants from the US
Department of Energy and the National Natural Science
Foundation of China (Grant No. NSFC-11174014). This
research used resources of the National Energy Research
Scientific Computing Center, which is supported by the Office
of Science of the U.S. Department of Energy under Contract
No. DE-AC02-05CH11231.
■
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